Aim of the Applet

Differentiate variations, permutations and combinations

Input data

• Elements to combining represented by letter or a number (total n)
• Number of elements to take p.
• Select whether imported or not the order of the elements.
• Indicate whether items can be repeated

Output data

Case Diagrams

      -Variations without repetition. Conditions: (p < n), care about the order and no repetitions.

      -Variations with repetition. Conditions: (p not equal n), care about the order and if there is repetition.

      -Combinations without repetition. Conditions: (p < n), no matter the order and there is no repetition.

      -Combinations with repetition. Conditions: no matter the order and there is repetition.

      -Permutations without repetition. Conditions: (p = n), care about the order and no duplicates.

      -Permutations with repetition. Conditions: (p = n), care about the order and repeated elements.

Results

      Used formula and total number of cases

The first steps

How many different 5 digit numbers can you do with the numbers (1,1,2,2,2)?

How many possible cases we have to roll two dice if the order does not matter? What if it matter?

How many ways can we order 4 different colors?